Explicit analytical solutions for liquid infiltration into capillary tubes: dynamic and constant contact angle.

Area of Science:

• Fluid dynamics
• Interface science
• Capillary phenomena

Background:

• The Lucas-Washburn theory describes capillary-driven liquid flow in tubes.
• Dynamic contact angles influence liquid infiltration dynamics.
• Understanding infiltration scenarios is crucial for various applications.

Purpose of the Study:

• To derive new analytical solutions for liquid infiltration into gas-filled capillary tubes.
• To generalize the Lucas-Washburn theory by incorporating a dynamic contact angle model.
• To identify and map different infiltration scenarios based on physical parameters.

Main Methods:

• Generalization of the Lucas-Washburn theory with a linear velocity-dependent dynamic contact angle model.
• Neglect of inertial forces, consistent with the original Lucas-Washburn approach.
• Derivation of explicit analytical solutions using the Lambert function.

Main Results:

• Explicit analytical solutions for interface position, velocity, and acceleration were obtained.
• Five distinct infiltration scenarios were identified: horizontal, upward (capillary rise), and three downward types (steady-state, accelerating, decelerating).
• Mutually exclusive conditions for each scenario were determined and visualized using 2D and 3D diagrams.

Conclusions:

• The derived analytical solutions accurately model liquid infiltration under dynamic contact angle conditions.
• The study provides a comprehensive framework for understanding and predicting capillary infiltration behavior.
• The solutions are valid for both dynamic and constant contact angle limits.